This work can be extended in several directions. A crucial test is to make sure that the qualitative picture is stable when the form of the cut-off function is modified. Moreover, to obtain the best numerical estimate of the critical exponent \(\) , the principle of minimal sensitivity (PMS) can be applied by studying the dependence of \(\)  on unphysical parameters, such as those which enter a class of cut-off functions or the values of inessential couplings, such as the vacuum energy. The PMS selects the value of \(\)  where this dependence is minimal (for a recent application of the PMS to the critical exponents of the Ising model see [1]}).
Furthermore, the dependence on the parameterisation of the metric tensor and the choice of gauge [2]}, [3]}, [4]}, [5]} can also be investigated within the minimal essential scheme. In the background field approximation, we neglect the running of these parameters, while a proper treatment of these parameters should identify them with inessential couplings since they cannot enter expressions for observables. Thus, going beyond the background field approximation, the minimal essential scheme should include extra gamma functions in order to impose renormalisation conditions for each unphysical parameter. As an alternative, one can use diffeomorphism and parameterisation invariant exact renormalisation equations, such as those based on the geometrical effective action [6]}, [7]} or the background independent exact renormalisation group [8]}.
